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Black-76 pricing for LME base metals

Base-metal options are priced on the forward with the Black-76 model. Here's what it needs, and the LME conventions that make the number actually correct.

Open the free Black-76 pricer →

Why Black-76 and not Black-Scholes

LME options are options on a forward (the metal for a given prompt date), not on a spot that pays no dividend. Black-76 is the variant of the Black-Scholes framework built for exactly that: it takes the forward price directly and discounts the result back from settlement. Use plain Black-Scholes with a spot and a carry fudge and you reintroduce an error that Black-76 avoids by construction.

The inputs it needs

• Forward — the metal's price for the option's prompt date (per tonne, USD).
• Strike — by price, or by delta against the smile.
• Volatility — ideally from a smile, so each strike uses the right point of the surface rather than one flat number.
• Time to expiry — driven by the LME calendar, not a round number of days.
• Discount rate — to bring the premium back from the settlement date.

The LME conventions that make it correct

The model is only half the job; the exchange's calendar is the other half:

• First-Wednesday expiry. LME options on a contract month expire on the first Wednesday of that month — not month-end.
• Third-Wednesday prompt. Exercise is into the third-Wednesday prompt future, which is the forward the option is written on.
• Premium discounting. The premium is handled on the exchange's own basis, so the discounting has to match to reconcile.

Miss any of these and the premium drifts from the exchange's — which is why a generic options calculator rarely agrees with the LME for a real base-metal option.

Checked against the LME's own calculator

PricerLab implements Black-76 with the LME's expiry, prompt and discounting conventions, and lines the output up against the exchange's own options calculator — so you can check the working, not just trust the number. It's free in the browser, with Greeks and multi-leg structures, no signup.

Price an option now →